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Using the generating function of SU(n) we find the conjugate state of SU(n)basis and we find in terms of Gel'fand basis of SU(3(n-1)) the representationof the invariants of the Kronecker products of SU(n). We find a formula for thenumber of the elementary invariants of SU(n). We apply our method to thecoupling of SU(3) and we find a new expression of the isoscalar of Wignersymbols ($\lambda 10,\lambda 2 \mu 2; \lambda 3 \mu 3$).

Applications of generating function method to the symmetry and the Kronecker products of SU(n) representations